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The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The numbers are

Correct Answer: 628, 372

Explanation:

Let us assume the numbers are a and b.
According to question,
a2 - b2 = 256000 .......................(1)
and a + b = 1000 .........................(2)
On dividing the Equation (1) with Equation (2),
(a2 - b2)/(a + b) = 256000/1000
(a2 - b2)/(a + b) = 256
(a + b)(a - b)/(a + b) = 256
a - b = 256...............................(3)
Add the equation (2) and (3), we will get
a + b + a - b = 1000 + 256
2a = 1256
a = 628
Put the value of a in equation (2), we will get
658 + b = 1000
b = 1000 - 628
b = 372
So answer is 628 , 372.


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